1. Section 2.3 Sine Law
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2. I) Sine Law
The Sine Law is for solving triangles that are not R.T.
Name each side with the opposite angle
There are 3 separate equations
The Sine Law can only be used when you are given one of the angles with its opposite side
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3. Ex: A triangle ABC has side a = 12 cm, angle A = 60°, and angle C = 45°. Solve for side c.

4. Practice: Find the value of “x”
Indicate the sides and angles
Formula
Cross Multiply and Solve for “X”
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5. II) Finding Missing Angles
To find the angle, you need to use inverse sine
If the angle is obtuse, you need to find the angle in Quadrant #2
Ex: Find the value of “θ” to the nearest degree
Indicate the sides and angles
Formula
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6. Example 2: A triangle has side a = 11 inches, angle A = 40°, and side c = 8 inches. Solve for angle C.

7. Practice: Find θ to the nearest degree
Formula
Formula
Angle “B” is an OBTUSE angle,
So it must be in Quadrant #2!!
Angle “B” is an OBTUSE angle,
So it must be in Quadrant #2!!
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8. Ex: The angle of elevation to the top of the tower is 43°
Ex: The angle of elevation to the top of the tower is 43°. If you travels 100m closer, the angle is 75°. How tall is the tower? Assume the person is about 1.5m tall.
Make a Triangle and Gather Info
Find the Hypotenuse of the triangle
Use the Hypotenuse to find the opposite side
Height of the Tower
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9. Example 7: At noon, two tracking stations on Earth , station A is 20 km west of station B, measure a rocket that was launched from a weather satellite. From station A the angle of elevation is 41° and from station B the angle of elevation was 75°. Find the height of the rocket above the earth. 9

10. Practice: A ship leaves Batumi on a bearing 300 and sails 860km
Practice: A ship leaves Batumi on a bearing 300 and sails 860km. They then change direction on a bearing of 222 and sail for 580km and reached Istanbul. How far is Batumi from Istanbul?
Turkey
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11. Proof For the Sine Law
If we use another altitude for angle A, we can solve for the other part of the sine law
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12. HW:
Assignment 2.3